In some probe-based data storage devices, the carrier of information is the presence or absence of topographical indentations, or “pits”, on a storage surface. Typically the presence of an indentation corresponds to a bit of value “1” while the absence of an indentation corresponds to a bit of value “0”. Each indentation is formed by application of a write signal which causes a probe of the device to deform the storage surface to create the indentation. For example, in AFM (Atomic Force Microscope)-based storage devices, the probe is a nanometer-sharp tip mounted on the end of a microfabricated cantilever. This tip can be moved over the surface of a storage medium in the form of a polymer film. A single indentation is formed by simultaneously applying a voltage pulse across certain terminals of the AFM cantilever and another voltage pulse between a substrate underneath the polymer film and a platform on the body of the cantilever. The first pulse heats a resistive element that heats the cantilever tip, while the second pulse creates an electrostatic force between the cantilever and substrate which forces the tip into the polymer film. These two pulses collectively form the write signal here, a single write signal being applied at each probe position on the storage surface where an indentation is to be created. In a read mode, the thermomechanical probe mechanism can be used to readback stored bits by detecting the deflection of the cantilever as the tip is moved over the pattern of bit indentations. AFM-based data storage is described in detail in IBM Journal of Research & Development, Volume 44, No. 3, May 2000, pp 323-340, “The ‘Millipede’—More Than One Thousand Tips for Future AFM Data Storage”, Vettiger et al., and the references cited therein. As described in this document, while basic read/write operations can be implemented using a single cantilever probe, in practice an integrated array of individually-addressable cantilevers is employed in order to facilitate increased data rates. Each cantilever of the array can read and write data within its own storage field as the array is moved relative to the surface of the storage medium.
For increased storage area density in probe-based devices, the indentations should preferably be placed close to each other. However, when the distance between indentations drops below a certain threshold, the indentations start to interact in a non-linear way. In particular, each newly created indentation partially “erases” previously-formed indentations spaced at a distance smaller than the threshold distance. The threshold distance, denoted by D and hereinafter also referred to as the indentation interference threshold, is dependent on the shape of the tip which penetrates the polymer film. The sharper the tip, the smaller D is. When the partially-erased indentations are read back, they correspond to a reduced signal amplitude compared to indentations which are not partially erased. These principles are illustrated in FIGS. 1a and 1b of the accompanying drawings. FIG. 1a shows two indentations written at the threshold distance D, where no interference occurs between indentations. FIG. 1b illustrates the partial erasing occurring when the spacing between indentations is reduced below the indentation interference threshold D, here to D/2. The later-formed indentation partially erases the former, resulting in the topography shown on the right-hand side of this figure. Vertical dotted lines indicate the timings at which the analog readback waveform corresponding to the written topography is sampled in each case, with the dots representing the corresponding sample values. In the FIG. 1a scenario, the correct readback sample values (1 1) are obtained. In FIG. 1b, however, the readback signal amplitude corresponding to the partially erased indentation has an intermediate level which is close to the detection threshold. In the presence of noise or other forms of distortion this sample value may easily shift above the threshold and be erroneously detected as “0”. This is illustrated in the figure where the written symbol values are 1 1 0 but the partial erasing results in readback sample values of 0 1 0. Thus, the noise margin of partially-erased indentations is reduced compared to non-erased indentations, leading to detection errors and hence loss of performance. It is therefore desirable to avoid partial erasing as far as possible.
One way to facilitate increased storage density and yet inhibit partial erasing is to resort to sharper tips. The sharpness of the tip determines the plastic radius surrounding each indentation, this being smaller for sharper tips. The plastic radius in turn determines how closely two indentations can approach each other before partial erasing occurs, i.e. D. Hence sharper tips lead to smaller indentation interference thresholds D. The problem with increasingly sharp tips, however, is that they are increasingly hard to fabricate. In particular, for large arrays of tips, tip homogeneity may be difficult for sharp tips compared to blunt tips. In addition, even if the above problems could be solved, sharp tips would not retain their sharpness for long, since tip wear due to rubbing of the tip against the storage medium would blunt the tip.
Another way to facilitate increased storage density while avoiding partial erasing is to use coding on the stored data. One family of codes that are used are the so-called (d, k) codes which ensure that consecutive “1's” in the coded bit sequence are separated by at least d, and at most k, “0's”, where the number d≧1. Since the physical distance between consecutive “1's”, or indentations, is limited to D, by artificially inserting d “0's” between the “1's” we can effectively decrease the symbol distance, that is, the distance between bits of the coded sequence, to D/(d+1) from the uncoded distance of D between information bits. FIG. 1c illustrates this concept for the case of d=1. Here, the distance between two consecutive “1's” is kept at the threshold distance D, but one coded bit of value “0” is introduced between them. In effect, therefore, the distance between code symbols is reduced to D/2, but there is no interference between indentations because the minimum distance between them is always D. A drawback of (d, k) codes is that not all possible sequences of “1's and “0's” are allowed in the coded bit-stream. In the case of d=1 codes, for example, the sequence 1 1 is not allowed. Consequently, there is an inherent rate loss associated with the coding process. This is quantified as the code rate R, a number less than one, which increases the effective symbol distance by 1/R. There is therefore an overall gain in storage density by a factor of R*(d+1) compared to the uncoded case. In the thermomechanical probe-storage system described above, for example, a (d=1, k=7) code has been chosen with a code rate R=2/3, offering a density increase of (2/3)*(2)=4/3. However, because of the code rate R<1, for a data rate r that the user sees, the electronics in the device has to process data at an internal rate of (r/R)>r. Thus, for a fixed IC technology, the user data rate of a coded system will be lower than that of an uncoded system. Coding of this form therefore trades storage density for user data rate.
Accordingly, it is desirable to provide a system for increasing storage density in probe-based data storage devices which can alleviate the drawbacks of existing systems discussed above.